The Irish international hooker has signed a two-year deal with the French club while Gelling returns to New Zealand to be closer to his family.
Leeds-born McIlorum has made 242 appearances for Wigan and was a stand-out performer for Ireland at the recent Rugby League World Cup.
Speaking to the club website, Wigan chairman Ian Lenegan said: "Several clubs expressed interest in Michael and we agreed that at this stage of his career it was right to allow him to explore his options.
"Several teams have put forward very favourable offers to Michael and we felt it right not to stand in his way.
"With Sam Powell and Thomas Leuluai both fine hookers and the encouraging performances of Josh Ganson last season we believe the time has come for Michael to move on and for Wigan to look to the future."
McIlorum added: "After speaking with Ian [Lenagan] it was made clear my future was elsewhere and with interest from a couple of clubs it was agreed now was the best time to part company.
"I would like to thank Ian and Kris [Radlinski] for making my time at Wigan successful and enjoyable."
Meanwhile Gelling, who has been one of the Warriors key players for a number of seasons, will also depart with the club saying they would not stand in the way of a player who wants to be closer to his family.
"I'm sad to see Anthony go," said Wigan head coach Shaun Wane.
"He has improved greatly during his time at Wigan and the coaching staff and I are proud of the progress he has made. He will be missed around the club and he leaves with our best wishes.
"From a squad perspective, we have known about this for a little while now which is why we acted swiftly to secure Dan Sarginson's return."